I don't know how you could identify a 'genuine' trans woman but being trans does not make you any more or less likely to commit crime than non trans who are the same sex ,
Being Trans does not make you more likely to commit crime, but it does give you easy access to women - and considering men as a sex are responsible for the vast majority of violent crime, it is not unreasonable for women to want spaces without men.
Self ID will allow any man to access women-only spaces. I as a women, do not want to share a space with any man with "lady feelings", and that goes for Eddie Izzard too!